Question

x² –3$\sqrt{3}$ x + 6 = 0

Answer 1

Given: x² –3$\sqrt{3}$ x + 6 = 0

On splitting the middle term –3$\sqrt{3}$ x as – $\sqrt{3}$ x – 2$\sqrt{3}$ x, we get:

$$\begin{gathered} x^2-\sqrt{3}x-2\sqrt{3}x+6=0 \\ \Rightarrow x\left(x-\sqrt{3}\right)-2\sqrt{3}\left(x-\sqrt{3}\right)=0 \\ \Rightarrow \left(x-\sqrt{3}\right)\left(x-2\sqrt{3}\right)=0 \end{gathered}$$

We know that if the product of two numbers is zero, then at least one of them must be zero.

Thus,

$$\begin{gathered} x-\sqrt{3}=0\mathrm{or}x-2\sqrt{3}=0 \\ \Rightarrow x=\sqrt{3}\mathrm{or}x=2\sqrt{3} \end{gathered}$$

Therefore, the solution of the given equation is x = $\sqrt{3},2\sqrt{3}$.